Automatic plotting of X-ray diffraction pole figures



J 1964 R. M. EICHHORN ETAL 3,117,226

AUTOMATIC PLOTTING OF X-RAY DIFFRACTION POLE FIGURES Filed July 18, 1960 Z 2 Sheets-Sheet 1 N 4 w ocrecroa XRAY SOURCE A AL QIIII A 1 3 /1 1. vim? SPEClMEN 2 I E IQTOR'S 8 ROBERT WEICHHORN GILBERT LADDIS "gm Mf- A TTORNE) Jan. 7, 964 R. M. EICHHORN ETAL 3,117,226

AUTOMATIC PLOTTING OF X-RAY DIFFRACTION POLE FIGURES Filed July 18, 1960 2 Sheets-Sheet 2" X-RAY POLAR DIFFRACTOMETER AM PUHER TRANSDUCER RECORDER X-RAY DIFFRACTOMETER AMPL'F'ER N DUCER CHOPPER INVENTORS ROBERT M.E|CHHORN GILBERT l. ADDIS United States Patent 3,117,226 AUTOMATIC PLOTTIN G 0F X-RAY DEFRACTION POLE FEGUPES Robert Milne Eichhorn, Westfieid, and Gilbert Irving Addis, Piainiield, Ni, assignors to Union Carbide Corporation, a corporation of New York Fiied July 18, 1960, Ser. No. 43,544 13 Claims. (Cl. ZSti-SLS) The present invention relates to an improved apparatus for plotting X-ray diffraction pole figures. More particularly it relates to an automatic system for directly plotting such figures so that iso-intensity areas are readily apparent.

In the study of the texture and preferred orientation in flat pieces or sheets of crystalline materials including metals, plastics, and rubber the pole figure diagram is commonly used. A pole figure is simply the stereographic sojection of the intercepts of the normals of one set of crystallographic planes with the reference sphere upon the reference plane, as will be more completely described later. The pole figure is used to describe the orientation of crystallographic planes the solid specimen with respect to its outside dimensions.

Preferred orientation information useful for plotting pole figures cm be obtained by X-ray diffraction by use of either photographic or counter techniques.

The procedure of obtaining sufficient X-ray diffraction data and its interpretation and plotting to describe preferred orientation by pole figures, when the photographic technique is used, is time consuming, laborious, and subject to considerable error. The time and effort required can be reduced, and the accuracy improved, by use of counter goniometers designed for this purpose.

Two types of pole figure goniometers have been used for this purpose. One scans the reference hemisphere in steps of elevation. An automatic recording device is available for this equipment but its cost is prohibitively high. Another type of goniometer scans the reference hemisphere in a spiral path. The instant invention is adapted for use with a. goniometer of the latter type.

The operation of X-ray diffraction goniometers or diifractometers is described in great detail in many pu'b lioations and US. Patents. US. Patent No. 2,798,957 describes the operation of a spiral scanning pole figure goniometer suitable for use with the present invention wherein the reference hemisphere is scanned in ever increasing increments of elevation from a horizontal reference plane.

As stated above the cost of automatic apparatus for directly plotting pole figures from the information obtained from such pole figure goniometers has been prohibitively high in fact no automatic plotting equipment is presently available for the spiral scanning pole figure goniometer. The alternative to such recorders has been to manually plot the pole figures from either a great many strip charts or a continuous strip chart which is both time consuming and tedious.

It is accordingly the object of the present invention to provide a method and apparatus for subjecting a specimen to scanning by X-rays over a continuous path, detecting the diffracted X-ray beam with a counter tube moving in such path in a reference hemisphere about the specimen, and processing such data to directly make a pole figure record.

It is a further object to produce such an apparatus which is relatively uncomplicated and inexpensive.

It is a still further object to produce such a device which is adaptable to a number of commercially available polar recorders.

Patented Jan. 7, 1964 Other objects and advantages will be apparent from the drawing in which:

FIG. 1 is a perspective view showing the geometrical relationship between a. sample and the resultant X-nay diffraction pattern on a reference hemisphere, and the equivalent pole figure.

FIG. 2 is a drawing representative of a record obtainable with one ern bodirnent of the present invention.

FIG. 3 is a drawing representative of a record obtained with a preferred embodiment of the present invention.

FIG. 4 is a schematic representative of a preferred chopper for use with the present invention.

FIGURE 5 is a block diagram showing the various components of a basic form of the instant device, and

FIG. 6 is a block diagram showing the various units comprising a preferred embodiment of the invention.

The objects of this invention are accomplished in general by an X-ray counter goniometer which scans the difiracted X-ray pattern in a spiral path upon a reference hemisphere and amplification means for said goniometer output. A polar recorder whose angular displacement is synchronized with the angular notation of the goniometer and whose radial displacement is synchronized with the elev-ational displacement of the goniometer is connected to the output of the amplifier through data processing me ans by which a record is produced Whose instantaneous recorded trace area is proportional to the intensity of the signal picked up by the goniometer.

In the preferred form of the invention, the last named means comprises a quantizer and chopper wherein the X-ray intensity signal from the amplifier is converted to a predetermined number of signal levels, for example four, and wherein each signal level from the quantizer causes the chopper to produce an output signal for the recorder which varies from no output at the first level to a continuous signal at the fourth level. Thus as the recorder traces out a spiral path, the stylus will either produce no trace, a dotted line, or a continuous line depending on the intensity of the X-rays picked up by the goniometer.

This invention is superior to all systems previously described because it is simpler and much cheaper than other pole figure recorders and much more rapid than manual plotting of data. It also directly and automatically produces a variable intensity pole figure. Specifically, it eliminates the replotting of data from strip charts onto a polar grid.

The invention will now be described in more detail with reference to the drawings.

While a highly detailed explanation of X-ray crystallography would not be feasible, briefly, the counter goniometer technique of investigating preferred orientation in crystalline matter consists of measuring directly the intensity of diffracted radiation from a particular family of crystallographic planes as a function of the specimen orientation with respect to incident X-radiation. The detector, usually a Geiger-Mueller tube, is set at the Bragg reflection angle for a specific reflection. Then the specimen is rotated systematically about two axes in order to scan the spatial distribution of diffracted intensity about the sample. Since the intensity of diffraction is directly related to the density of poles, and the orientation for diffraction corresponds to the orientation of poles, the distribution of intensity can be related to the distribution of density of poles.

As shown in FIG. 1, all of the planes in the small crystalline specimen at the center of the reference sphere can be made to diifract energy into the top hemisphere if the specimen is gyrated through all orientations with respect to the incident X-ray beam. The normal to any set of planes when they are in reflecting position intersects the sphere and this intersection is called a pole or the pole of the reflecting planes.

A pole figure is the stereographic projection of points on a reference hemisphere described about the specimen. For example the diffracted X-ray beam pole areas 2 and 4 on the reference sphere become the pole figure 2 and 4' when projected on the equatorial plane of the reference sphere in the manner described. It should be noted that this pole figure has been greatly simplified for purposes of illustration, and that in actuality they can be far more complicated and have a number of different intensity levels in each area.

In order to scan the top hemisphere, the counter tube or detector may be rotated about two axes so that it races out a spiral path upon the surface of the hemisphere. Alternatively, the specimen may be gyrated so as to produce the same relative motion. The latter method is used in practice due to its greater mechanical simplicity. This spiral trace has not been illustrated as it is thought to be obvious. It is accomplished by constantly rotating the specimen about its vertical axis and at the same time, continually and linearly rotating the specimen about a horizontal axis. For example, for every 360 of rotation about its vertical axis the elevation is increased 10 until a desired portion of the sphere has been scanned.

Due to the nature of the projection, the plane spiral on the two dimensional plot has non-constant pitch which increases with increasing radial position. The pitch of .the plane spiral, drawn by the polar recorder employed,

may be made either constant (convenient) or non-con stant (accurate) by use of an appropriate linear or nonlinear radial trace displacing means in said polar recorder,

As the goniometer or detector scans the reference hemisphere along such spiral path the recorder is adapted to generate and plot a plane spiral in synchronism. When the counter tube picks up a localized reflection it is fed thru amplifier and scaler circuits in the X-ray equipment and appears on the polar plot as a change in the character of the spiral trace.

As may be readily understood the X-ray intensity information could be placed on the spiral plot having conventional amplitude variations, however it is the object of this invention to give a direct visual indication of intensity in the pole figures which would not be possible with amplitude modulation. According to the present invention the trace must be modulated by a system which will give the impression of varying intensity of the trace within a given area. The use of pulse or frequency modulation has been found to provide satisfactory results giving the desired impression of a shaded contour map.

FIG. 2 illustrates a trace obtained using frequency modulation where the areas of greater trace density repre sent greater signal strengths and higher frequency. Many transducers are available for obtaining an amplitude to frequency conversion such as a system wherein the frequency of an oscillator is varied by a varying amplitude signal fed to a reactance circuit which would proportionally change the frequency of the oscillator.

FIG. 3 illustrates a trace obtained with the preferred embodiment of the invention which is pulse modulation. In this embodiment the trace intensity and overall plot density vary inversely with the frequency of the pulses or more particularly the number of discontinuities. For example, maximum density is represented by a solid trace and minimum density or no signal detected is represented by complete absence of the trace. Gradations between minimum and maximum density are shown by an increasing recorder duty cycle. By duty cycle is meant the fraction of the period of a recording cycle during which the marking means is actuated. A preferred apparatus for obtaining this type of trace will be described subsequently.

The invention will now be described in greater detail with reference to FIG. 5 which is a block diagram of a basic form of the apparatus. The X-ray ditfractometer referred to in the first block is of a type exemplified by an RCA pole figure goniometer which has a source of collimated X-rays and a Geiger counter or the like.

The essential features include provisions for continuous rotation of the specimen about a vertical axis and about a horizontal axis. It is to be understood that vertical and horizontal refer to the equatorial plane of the reference sphere and hence are relative to said plane. If said plane were not horizontal the two above axes would change accordingly. These two movements may easily be synchronized with the movements of a polar chart recorder by the proper selection of synchronous motors and gear ratios.

The specimen is mounted in the center of a large ring which can be continuously rotated through 360 by synchronous motor and gear drive means. This rotation corresponds to the B angle rotation of FIG. 1. The plane of the ring may also be rotated through thereby changing the elevational attitude of the specimen with respect to the incident X-rays. This rotation corresponds to the at angle of FIG. 1 and may be accomplished by'a separate synchronous motor or by appropriate gearing to the first motor. As will be understood in this apparatus the spiral trace of the reference hemisphere is achieved by rotating the specimen and maintaining the X-ray source and detector stationary.

Operation of the pole figure recorder in FIG. 5 is based on synchronizing the location in a stereographic projection, with corresponding orientation of the sample. In the simplest form of the invention the circular chart on a conventional polar recorder turntable is rotated about its center at the rate of one revolution per one revolution of the specimen mounting ring and thus, in synchronism with the B-rotation of the specimen. By choosing proper synchronous motors and gear ratios this synchronism can easily be achieved by one skilled in the art. The pen or stylus can be moved along the radius of the chart, by such conventional means as a rotating screw and follower with the stylus in a suitable track or carriage driven by the follower. A stylus arm pivoted at one end and driven by a cam can also be used to impart the desired radial movement of the stylus. The particular marking system utilized with the stylus will be described later in the specification. The radial movement of the stylus must be synchronized with the rotation of the plane of the specimen ring or the a rotation of the specimen goniometer. In this instance the synchronization comprises selecting the relative speeds of the two drives such that the same length of time is required for the recorder stylus to make its traverse from its outer most point to the origin or center of the chart as it takes for the specimen goniometer to make the full 0-90 at angle traverse. It will be noted in both FIGURES 2 and 3 that the trace be- 1 gins at the outside of the record which corresponds to an at angle of 0.

The a and B angles are indicated three dimensionally in FIG. 1 and two dimensionally in FIG. 3.

The block labelled transducer which is shown asa separate element is in actuality inter-dependent on the type of polar recorder used and vice versa. The essential feature of the transducer which is important to the instant invention is that it must convert the amplitude signal from the detector and amplifier to an output signal which, in cooperation with the particular recorder used,

will produce a trace having apparent intensity variation. The two systems of frequency and pulse modulation described above are exemplary, however, the invention is not intended to be limited thereby.

In the frequency modulation system, the voltage signal which is proportional to the intensity of the X-ray reflection may be applied to a voltage sensitive device which yields an output frequency proportoinal to input voltage, as described previously. An example of a commercially available unit is the Voltage to Frequency Converter made by Dynac Inc. of Palo Alto, California. Superposition of the variable frequency output on the spiral trace of the recorder results in variation of apparent line density with changing X-ray intensity as shown in FIG. 2. The overall appearance would be one of shaded dark areas corresponding to areas of high X-ray diffraction intensity.

This sort of data presentation system must be used with a recorder capable of responding to the trace frequencies employed. A convenient form of recorder for this embodiment is one in which the basic spiral trace is imparted to the record by rotating the record paper by an appropriate drive means as discussed previously and moving the stylus arm by a mechanical means such as cam or screw thread to impart the basic spiral trace and wherein additional radial movement of the stylus is achieved by a high frequency responsive electro-magnetic system similar to a DArsonval meter movement actuated by the signal from the detector and voltage to frequency transducer. Since such recorders are well known it is not thought necessary to detail the operation of same. It is of course understood that the rotary motion .of the recorder chart is synchronized with the B angle rotation (rotation about the vertical axis) of the specimen goniometer and that the radial displacement of the spiral trace is synchronized with the at angle displacement of the specimen goniometer.

The frequency modulation data display system could also be used with an XY recorder having a spiral trace generating source. The same necessity for synchronization of the recorder movements with the pole figure goniometer would also apply. The resultant pole figures obtainable would be the same. The primary advantage being that the equipment investment is much lower with an XY recorder.

Essentially the same type of shaded pole figure diagram can be prepared by pulse modulation as with frequency modulation. This type is the preferred form of the invention and is preferred since it represents a very basic apparatus which gives excellent results while utilizing parts readily available.

FIG. 6 is a block diagram of a preferred embodiment of a pulse modulated pole figures recorder system.

The block labeled X-ray diffractometer is the same type of automatic specimen goniometer set forth with respect to FIG. 5 including a collimated X-ray source, pick up means such as a Geiger tube and drive means for the specimen for tracing out the effective spiral trace upon the reference hemisphere discussed at length previously.

The block labeled amplifier amplifies the output from the Geiger counter tube and converts it into a conventional amplitude modulated signal indicative of the intensity of detected X-ray reflections or diifractions.

The block labeled transducer in this preferred embodiment comprises a Leeds and Northrup strip recorder of the slide wire potentiometer type. This recorder is typical of a number of commercially available units whose operation is well known. Briefly the slide wire positioner, a drum in this case, is moved by an appropriate servo system to a position such that the voltage drop thereacross produces a feedback voltage which is equal to or balances out the input signal and which mechanical displacement also drives the recording stylus transverse to the direction of movement of the strip chart. Means are additionally provided for connecting the said slide wire drum to an external shaft for accomplishing additional control func tions. It is the external shaft drive which is utilized to set the chopper for proper duty cycle in the present embodiment.

Referring more particularly to FIG. 4 for a description of the chopper, a 0-10 mv. signal from the X-ray amplifier is applied to the 0-10 mv. slide wire recorder. The chopper comprises a cam and shaft 1% which are mechanically attached to the slide wire drum 12 of the recorder 8 and adjusted to actuate four microswitches .14, 16, 18 and 20 as follows:

Mv. Switch 14, closed 02;0 Switch 16, closed 2.05.0 Switch 13, closed 5.08.0 Switch 20, closed -100 An auxiliary motor 22 operating at 12 r.p.m. is'used to drive another set of 4 earns 24 and microswitches 26 used as choppers. The cams are adjusted to actuate the microswitches for varying percentages of the cycle with on time increasing with the number of the cam.

PEG. 3 illustrates a trace using the four conditions above, between 0 and 2.0 mv. there is no trace; between 2.0 and 5.0 mv. there are four short dashes; between 5.0 and 8.0 mv. there are two longer dashes; and between 8.0 and 10.0 mv. the trace is continuous.

It will, of course, be understood that the number of chopper cams and microswitches can be increased or decreased. The number required depends on the amount of resolution desired in the plot.

The instant chopper could be used with any polar recorder capable of making a discontinuous trace. For example, an inking stylus and a pen lift relay (indicated at 28 in FIG. 4) equipped polar recorder would be suitable wherein the radial displacement which traces the spiral can be achieved by driving the stylus arm with a suitably synchronized cam or rotating screw and follower assembly. Alternatively, if the recorder is equipped with electro-sensitive paper the stylus is connected in series with the chopper microswitches and a trace is effected when current passes through the electro-sensitive paper, the discontinuities being effected as the current ceases.

While the above system could be used with any polar recorder capable of producing a spiral trace the use of an XY recorder having a spiral time-base generator associated therewith is preferred since this combination .provides a very inexpensive and readily available apparatus. Such a recorder is described in detail in US. patent appli cation No. 766,817 of L. A. Rosenthal, filed October 13, 1958, and will be referred to hereinafter as a spiral time base XY recorder.

Briefly the spiral generator comprises-a motor which is chosen to run at a speed corresponding to one sweep cycle in time, driving a sine-cosine potentiometer such as manuf actured by Gmewell Co., Newton Falls, Mass., or F. W. Sickles Co., Chicopee, Mass. A linear potentiometer has its output connected to the sine-cosine potentiometer. The movable contact on the linear potentiometer is driven by suitable means (usually the same motor that drives the sine-cosine potentiometer) which supplies a varying voltage to the sine-cosine potentiometer. This varying voltage causes the spiral trace as will be explained. A slip clutch prevents injury to the linear potentiometer at its limits of travel, and also allows for an initial setting of the radial position of the X--Y coordinate.

The sine-cosine potentiometer in its simplest form oomprises a fiat resistance card winding to which is connected a direct current source, in this case, the voltage from the linear potentiometer. This causes current to flow through the resistance card setting up an electric field proportional to the current therethrough. Brushes physically displaced by pick off two quadrature voltages as the resistance card is rotated, the voltages picked off vary as a sine function and cosine function. For a more detailed discussion of the operation of a sine-cosine potentiometer, reference is made to the Components Handbook, by Blackburn, vol. 17 of M.I.T. Radiation Series, published by McGraw-Hill Co., Inc.

If the potential of the voltage supplied to the sine cosine potentiometer is maintained at a constant level and the resistance card is rotated and the two outputs fed to an XY recorder (such as the X-Y Plotter of the Electro Instruments Co., San Diego, California) a circle will be plotted. If the input to the sine-cosine potentiometer is varied linearly a spiral is developed. Thus, as applied to the instant invention, the brushes for picking quadrature voltages off the sine-cosine potentiometer are driven in synchronism with the B angle scanning means of the specimen goniometer, and the movable contact on the linear potentiometer is driven in synchronism with the at angle or elevational displacement drive means of said goniometer. As will be understood, if it is desired to make the spiral pitch non-constant for an accurate pole figure, the potentiometer itself may be made non-linear or the drive means for the contact may be made to move in a non-linear manner as by a suitably shaped cam.

The X-Y recorder may be equipped with an inking stylus and a pen lift relay or utilize electro-sensitive paper as discussed above for use with the pulse modulation system. If the frequency modulation system is to be used, a load resistor is placed electrically between the output of the linear potentiometer and the input of the sine-cosine potentiometer and the output of the frequency modulation transducer is impressed across the sine-cosine potentiometer with the same trace as disclosed above with reference to FIG. 2. With this latter system a continuously recording stylus system is, of course, used.

In the operation of the preferred embodiment of the invention shown in FIG. 6 an X-ray intensity signal is picked up by the detector tube of the specimen goniometer and fed as a series of pulses to the amplifier which amplifies the signal and converts it to an amplitude varying intensity signal which is in turn fed to the Leeds and Northrup strip recorder which, as stated above, is used merely as a convenient means to convert the electric signal to a mechanical one. The mechanical movement of the slide-wire drum on the strip recorder selects a particular cam and microswitch circuit in the chopper as shown in FIG. 4 depending on the amplitude of the signal from the amplifier. The pulsed output from the chopper is then used to operate the pen lift relay of the XY recorder. The spiral generator equipped X-Y recorder is synchronized with the specimen goniometer in essentially the same manner that the more conventional polar recorder described above is synchronized. The driving 'cams for moving the brushes across the sine-cosine potentiometer is synchronized, preferably by the use of synchronous motors, with rotation of the specimen ring per se or the B angle displacement so that 360 of rotation of the specimen ring is accompanied by a 360 rotation of the sine-cosine potentiometer brushes. The means for rnoving the contact on the linear potentiometer is synchronized with rotation of the specimen ring plane from 90 or 06 angle displacement. Thus as the specimen goniometer begins its trace at an at angle of 0 the linear potentiometer feeds maximum voltage to the sine-cosine potentiometer which is decreased to zero voltage as the at angle increases to its maximum of 90. The resultant plot is the pulse modulated spiral of FIG. 3.

The system above-described automatically plots complete 'pole figure density diagrams. No manual plotting of the pole figure from a series of strip charts is required nor is it necessary to manually draw in iso-intensity lines on a polar chart wherein colored iso-intensity points are charted as in one extremely expensive commercial apparatus. The system is further composed of individually available commercial components of quite reasonable price. The end results are considered superior to those obtainable with systems costing many times more than the instant unit.

It is obvious from the specification and description that a number of modifications and substitutions could be made by a person skilled in the art without departing from the spirit and scope of the invention. For example, a number of different polar recorders and stylus actuating systems could be used in addition to those recorders described herein. Also there are alternatives to the chopper cams and microswitches. A commutator and brush assembly, hole and brush assembly or photocell and slotted shutter means could be used as the pulse source.

What is claimed is: 1. A device for automatically plotting X-ray diffraction pole figures which comprises an automatic pole-figure goniometer having a source of collimated X-rays, X- ray detector means adapted for scanning the pole-figure reference hemisphere in a spiral path, amplifier means connected to the detector, recorder means for generating a spiral trace in synchronism with the scanning pattern of the automatic pole figure goniometer, and means effective in combination with said recorder for producing an increased trace area per unit area of the recorder sheet as the signal from the detector increases in magnitude.

2. A plotting device as set forth in claim 1 wherein the last named means produces a continuous constant amplitude frequency modulated trace whose frequency is directly proportional to the intensity of the detected X-ray beam.

3. A plotting device as set forth in claim 1 wherein the last named means produces a discontinuous trace whose duty cycle is directly proportional to the intensity of the detected X-ray beam.

4. A plotting device as set forth in claim 3 wherein the recorder has X and Y signal inputs which are supplied from a spiral generating sine-cosine potentiometer which is driven in synchronism with the scanning pattern of the pole figure goniorneter.

5. A plotting device as set forth in claim 3 wherein said last named means is a pulse forming network which comprises a plurality of switch means each having a different duty cycle connectable in series with the recorder stylus activating means and means for selecting one of said switch means according to the magnitude of the detected X-ray signal.

6. A plotting device as set forth in claim 5 wherein the switching means comprises a plurality of commutators and brushes and the selecting means comprises a plurality of microswitches actuated by a cam rotatable in accordance with the magnitude of the detected X-ray signal.

7. A device for automatically plotting pole figures which comprises an automatic pole figure goniometer having a source of collimated X-rays, X-ray detector cans adapted for scanning the pole figure reference hemisphere in a spiral path, amplifier means connected to the detector output for producing a signal whose amplitude is proportional to the intensity of the detected X-ray beam, means connected to the input of the amplifier means for converting the amplitude varying signal to a constant amplitude frequency modulated signal wherein the frequency of the output is proportional to said amplifier output signal, recorder means connected to the output from said last named means for generating a spiral trace in synchronism with the pole figure goniometer and for superimposing the said frequency modulated signal on the spiral trace and recording same and wherein the amplitude of the recorded signal is not more than half the distance between adjacent traces.

8. A device for automatically plotting pole figures which comprises an automatic pole figure goniometer having a source of collimated X-rays, X-ray detector means adapted for scanning the pole figure reference hemisphere in a spiral path and having an output proportional in magnitude to the intensity of the detected X-ray beam, ampliiier means connected to the output from the detector which produces an output signal whose amplitude is proportional to the detected X-ray signal, servomechanism means connected to the output of the amplifier for converting said output to a proportional mechanical displacement, means comprising a camshaft for closing one of a plurality of associated switches in accordance with said mechanical displacement, pulse forming means in series with each said switch having a difierent duty cycle; a polar recorder adapted to produce a spiral trace, the rotational displacement of the recorder being synchronized with the rotational displacement about the axis of the equatorial plane of the reference hemisphere of the pole figure by the detector means and the radial displacement of the recorder being synchronized with the elevational displacement from the equatorial plane of the said hemisphere by the detector means, wherein the recorder has a stylus which is actuated by the particular pulse forming means selected by the switch means actuated by the said mechanical displacement.

9. A plotting device as set forth in claim 8 wherein the pulse forming means comprises a plurality of rotatable circuit interruptors wherein the duty cycle is determined by the number of interruptions occurring per rotation.

10. A plotting device as set forth in claim 9 wherein each circuit interruptor comprises the combination of a cam and a normally closed microswitch which is caused to open by an appropriate number of equidistantly spaced lobes on the cam.

11. A plotting device as set forth in claim 8 wherein the polar recorder comprises a spiral time base XY recorder.

12. A device for automatically plotting pole figures which comprises an automatic pole figure goniometer having a source of collimated X-rays, X-ray detector means adapted for scanning the pole figure reference hemisphere in a spiral path, a spiral trace generating recorder wherein the rotational displacement of said trace is synchronized with the rotational displacement of the spiral scanning path of said goniometer and wherein the radial displacement of said spiral recorder trace is synchronized with the 1% elevational displacement of the spiral scanning path of said goniometer, and means for amplifying the signal from the detector and means effective in combination with said recorder to produce an increased trace area per unit area of the recorder sheet as the detected X-ray signal from said amplifier increases in magnitude.

13. A plotting device as set forth in claim 12 wherein the recorder has balanced X and Y inputs and has suitably driven linear potentiometer and sine-cosine potentiometer spiral trace generating means wherein the sinecosine potentiometer drive means is synchronized with the rotational displacement of the spiral scanning path of the goniometer and the drive means for the linear potentiometer is synchronized with the elevational displacement of the spiral scanning path of said goniometer.

References Cited in the file of this patent UNITED STATES PATENTS Geisler 'Aug. 28, 1956 Bond Jan. 7, 195 8 FOREIGN PATENTS Great Britain Aug. 17, 19 60 OTHER REFERENCES A Spiral-Scanning X-Ray Reflector Goniometer for the Rapid Determination of Preferred Orientations, by A. N. Holden, from the Review of Scientific Instruments, vol. 24, No. 1, January 1953, pp. 10, 11, 12. 

1. A DEVICE FOR AUTOMATICALLY PLOTTING X-RAY DIFFRACTION POLE FIGURES WHICH COMPRISES AN AUTOMATIC POLE-FIGURE GONIOMETER HAVING A SOURCE OF COLLIMATED X-RAYS, XRAY DETECTOR MEANS ADAPTED FOR SCANNING THE POLE-FIGURE REFERENCE HEMISPHERE IN A SPIRAL PATH, AMPLIFIER MEANS CONNECTED TO THE DETECTOR, RECORDER MEANS FOR GENERATING A SPIRAL TRACE IN SYNCHRONISM WITH THE SCANNING PATTERN OF THE AUTOMATIC POLE FIGURE GONIOMETER, AND MEANS EFFECTIVE IN COMBINATION WITH SAID RECORDER FOR PRODUCING AN INCREASED TRACE AREA PER UNIT AREA OF THE RECORDER SHEET AS THE SIGNAL FROM THE DETECTOR INCREASES IN MAGNITUDE. 